Using the following ANOVA summary table, what F-ratio is obtained for these data, and is it significant at the .05 alpha level? $\begin{array}{|l|l|l|l|l|}
\hline \text { Source of variation } & \text { SS } & \text { df } & \text { MS } & \text { F } \
\hline \text { Between } & 270 & 9 & & \
\hline \text { Within } & 5600 & 560 & & \
\hline \text { Total } & & & & \
\hline
\end{array}$
A) 1.0, not significant
B) 2.0, not significant
C) 3.0, significant
D) 4.0, significant

Question

Quizplus · Accepted Answer

To find the F-ratio, we divide the MS between by the MS within. So, we need to fill in those values in the ANOVA table. We can find the MS between by dividing the SS between by its degrees of freedom (df), which is 9. MS between = SS between / df between = 270 / 9 = 30. We can find the MS within by dividing the SS within by its df, which is 560. MS within = SS within / df within = 5600 / 560 = 10. Now we can calculate the F-ratio by dividing MS between by MS within: F = MS between / MS within = 30 / 10 = 3. Since we have 9 numerator degrees of freedom and 560 denominator degrees of freedom, we can look up the critical F-value in a table (or use software) to determine if the F-ratio is significant at the .05 level. At the .05 level, the critical F-value with 9 and 560 degrees of freedom is 1.94. Since our obtained F of 3.0 is greater than this critical value, we reject the null hypothesis and conclude that there is a significant difference between the group means. Therefore, the answer is C.

Using the Following ANOVA Summary Table, What F-Ratio Is Obtained